TL;DR
This paper generalizes semi-infinite cohomology for Lie algebras lacking a semi-infinite structure, clarifies affine W-algebras for nilpotent elements, and introduces affine W-algebras for admissible pairs.
Contribution
It extends semi-infinite cohomology to broader Lie algebra classes and refines the definition of affine W-algebras for nilpotent elements and admissible pairs.
Findings
Extended semi-infinite cohomology to non-structured Lie algebras
Clarified affine W-algebras for general nilpotent elements
Defined affine W-algebras for admissible pairs
Abstract
We extend the notion of semi-infinite cohomology of Lie algebras to include cases where the Lie algebra does not admit a semi-infinite structure but satisfies a mild condition. Our construction clarifies the definition of affine W-algebras in general nilpotent elements case given by V. Kac, S. Roan and M. Wakimoto. We will also give a characterization of admissible pairs with respect to a nilpotent element in a semisimple Lie algebra and define affine W-algebras associated to admissible pairs, while finite W-algebras associated to admissible pairs were already introduced before.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Homotopy and Cohomology in Algebraic Topology